Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential

Dong Han Kim, Lingmin Liao, Michal Rams +1

Let $((0,1],T)$ be the doubling map in the unit interval and $\phi$ be the Saint-Petersburg potential, defined by $\phi (x)=2^n$ if $x\in (2^{-n-1},2^{-n}]$ for all $n\ge 0$. We consid…